Question: Find the intersection of the lines $9x-4y=30$ and $7x+y=11.$ Express your answer as an ordered pair $(x,y).$
We can find $x$ by taking four times the second equation plus the first: $$4(7x+y)+(9x-4y)=28x+9x=37x=4(11)+30=74\implies x=2.$$Substituting into the second equation, we can find $y:$ $$7x+y=11\implies y=11-7x=11-7(2)=-3.$$Thus our answer is $\boxed{(2,-3)}.$